Short answers, pulled from the story.
Tlepolemus was a son of Heracles and the leader of the Rhodian contingent in the Trojan War. Ancient sources name his mother as either Astyoche, daughter of Phylas king of Ephyra, or Astydameia, daughter of Amyntor or Ormenus. He appears in Homer's Iliad, where he is killed by the Lycian commander Sarpedon.
Tlepolemus fled to Rhodes after killing Licymnius, the aged maternal uncle of Heracles. The Bibliotheca describes the death as an accident; Pindar states that the killing was intentional and driven by anger.
Tlepolemus founded Cameirus, Ialysus, and Lindus on the island of Rhodes. He divided Rhodes into three portions and established each as a separate city-state. He was accompanied to Rhodes by his wife Polyxo, a woman of Argive origin.
Tlepolemus had been listed by Hyginus among the suitors of Helen of Sparta, which bound him by the oath of Tyndareus. That oath required every former suitor to defend Helen's chosen husband against any challenger. Tlepolemus sailed to Troy with nine ships from Rhodes.
Tlepolemus died fighting Sarpedon, the Lycian commander, on the first day of battle recounted in the Iliad. He taunted Sarpedon by questioning his courage and his divine parentage as a son of Zeus, then attacked. Tlepolemus wounded Sarpedon with his spear but was killed by Sarpedon's return blow.
According to Pausanias, Polyxo, the wife of Tlepolemus, arranged the death of Helen of Sparta to avenge her husband. Polyaenus recorded a rival version in which Menelaus disguised a servant as Helen, the Rhodians killed the servant by mistake, and Menelaus and Helen escaped.